Minimum value of K such that each substring of size K has the given character

Given a string of lowercase letters S a character c. The task is to find minimum K such that every substring of length K contains the given character c. If there is no such K possible, return -1.
Examples:

Input: S = “abdegb”, ch = ‘b’
Output: 4 
Explanation:
Consider the value of K as 4. Now, every substring of size K(= 4) are {“abde”, “bdeg”, “degb” } has the character ch(= b’).

Input: S = “abfge”, ch = ‘m’
Output : -1

Naive Approach: The simplest approach to solve the given problem is to iterate for all possible sizes of substrings over the range [1, N] and check which minimum value of K satisfies the given criteria. If there doesn’t exist any such value of K, then print “-1”.

Implementation:- 

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
//Function to check character c in all substring of size i in s
bool ispresent(int i,string s,char c)
{
      int j=0;

      //map to store the elements which are present in current substring
      //of length i
      unordered_map<int,int> mm;
      //iterating over all length string of size i
      for(int k=0;k<s.length();k++)
    {
          mm[s[k]]++;
          if(k-j+1==i)
        {
              //if character c is not present return false
              if(mm==0)return false;
              mm[s[j]]--;
              j++;
        }
    }
  return true;
}

// Function to find the minimum value
// of K such that char c occurs in all
// K sized substrings of string S
int findK(string s, char c)
{
      //Loop for substring of size 1 to N
      for(int i=1;i<=s.length();i++)
    {
          //if all substring of size i have charachetr c
          if(ispresent(i,s,c))return i;
    }
  return -1;
}

// Driver Code
int main() {
    string S = "abdegb";
    char ch = 'b';
    cout<<(findK(S, ch));
    return 0;
}


// This code is contributed by shubhamrajput6156

Output

4

Time Complexity: O(N^2)
Auxiliary Space: O(N)

Efficient Approach: The above approach can also be optimized by using an observation that the minimum value of K is equal to the maximum difference between the consecutive occurrences of the given character ch as for every substring of size K there must have at least 1 character as ch. Follow the steps below to solve the given problem:

• Initialize a variable, say maxDifference as -1 that store the resultant value of K.
• Initialize a variable, say previous as 0 that store the previous occurrence of the character ch in the string S.
• Traverse the given string S using the variable i and if the current character is ch then update the value of maxDifference to the maximum of maxDifference and (i – previous) and the value of previous to i.
• After completing the above steps, print the value of maxDifference as the result.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find the minimum value
// of K such that char c occurs in all
// K sized substrings of string S
int findK(string s, char c)
{

    // Store the string length
    int n = s.size();

    // Store difference of lengths
    // of segments of every two
    // consecutive occurrences of c
    int diff;

    // Stores the maximum difference
    int max = 0;

    // Store the previous occurrence
    // of char c
    int prev = 0;

    for (int i = 0; i < n; i++) {

        // Check if the current character
        // is c or not
        if (s[i] == c) {

            // Stores the difference of
            // consecutive occurrences of c
            diff = i - prev;

            // Update previous occurrence
            // of c with current occurrence
            prev = i;

            // Comparing diff with max
            if (diff > max) {
                max = diff;
            }
        }
    }

    // If string doesn't contain c
    if (max == 0)
        return -1;

    // Return max
    return max;
}

// Driver Code
int main() {
    string S = "abdegb";
    char ch = 'b';
    cout<<(findK(S, ch));
    return 0;
}


// This code is contributed by 29AjayKumar

Java

// Java program for the above approach
class GFG {

    // Function to find the minimum value
    // of K such that char c occurs in all
    // K sized substrings of string S
    public static int findK(String s, char c)
    {

        // Store the string length
        int n = s.length();

        // Store difference of lengths
        // of segments of every two
        // consecutive occurrences of c
        int diff;

        // Stores the maximum difference
        int max = 0;

        // Store the previous occurrence
        // of char c
        int prev = 0;

        for (int i = 0; i < n; i++) {

            // Check if the current character
            // is c or not
            if (s.charAt(i) == c) {

                // Stores the difference of
                // consecutive occurrences of c
                diff = i - prev;

                // Update previous occurrence
                // of c with current occurrence
                prev = i;

                // Comparing diff with max
                if (diff > max) {
                    max = diff;
                }
            }
        }

        // If string doesn't contain c
        if (max == 0)
            return -1;

        // Return max
        return max;
    }

    // Driver Code
    public static void main(String args[]) {
        String S = "abdegb";
        char ch = 'b';
        System.out.println(findK(S, ch));

    }
}

// This code is contributed by saurabh_jaiswal.

Python3

# python program for the above approach

# Function to find the minimum value
# of K such that char c occurs in all
# K sized substrings of string S
def findK(s, c):

    # Store the string length
    n = len(s)

    # Store difference of lengths
    # of segments of every two
    # consecutive occurrences of c
    diff = 0

    # Stores the maximum difference
    max = 0

    # Store the previous occurrence
    # of char c
    prev = 0

    for i in range(0, n):

        # Check if the current character
        # is c or not
        if (s[i] == c):

            # Stores the difference of
            # consecutive occurrences of c
            diff = i - prev

            # Update previous occurrence
            # of c with current occurrence
            prev = i

            # Comparing diff with max
            if (diff > max):
                max = diff

    # If string doesn't contain c
    if (max == 0):
        return -1

    # Return max
    return max


# Driver Code
if __name__ == "__main__":

    S = "abdegb"
    ch = 'b'
    print(findK(S, ch))

# This code is contributed by rakeshsahni

C#

using System.Collections.Generic;
using System;
class GFG
{

    // Function to find the minimum value
    // of K such that char c occurs in all
    // K sized substrings of string S
    public static int findK(string s, char c)
    {

        // Store the string length
        int n = s.Length;

        // Store difference of lengths
        // of segments of every two
        // consecutive occurrences of c
        int diff;

        // Stores the maximum difference
        int max = 0;

        // Store the previous occurrence
        // of char c
        int prev = 0;

        for (int i = 0; i < n; i++) {

            // Check if the current character
            // is c or not
            if (s[i] == c) {

                // Stores the difference of
                // consecutive occurrences of c
                diff = i - prev;

                // Update previous occurrence
                // of c with current occurrence
                prev = i;

                // Comparing diff with max
                if (diff > max) {
                    max = diff;
                }
            }
        }

        // If string doesn't contain c
        if (max == 0)
            return -1;

        // Return max
        return max;
    }

    // Driver Code
    public static void Main()
  {
        string S = "abdegb";
        char ch = 'b';
        Console.WriteLine(findK(S, ch));

    }
}

// This code is contributed by amreshkumar3.

Javascript

<script>
// Javascript program for the above approach

// Function to find the minimum value
// of K such that char c occurs in all
// K sized substrings of string S
function findK(s, c)
{

  // Store the string length
  let n = s.length;

  // Store difference of lengths
  // of segments of every two
  // consecutive occurrences of c
  let diff;

  // Stores the maximum difference
  let max = 0;

  // Store the previous occurrence
  // of char c
  let prev = 0;

  for (let i = 0; i < n; i++) {
    // Check if the current character
    // is c or not
    if (s[i] == c) {
      // Stores the difference of
      // consecutive occurrences of c
      diff = i - prev;

      // Update previous occurrence
      // of c with current occurrence
      prev = i;

      // Comparing diff with max
      if (diff > max) {
        max = diff;
      }
    }
  }

  // If string doesn't contain c
  if (max == 0) return -1;

  // Return max
  return max;
}

// Driver Code

let S = "abdegb";
let ch = "b";
document.write(findK(S, ch));

// This code is contributed by saurabh_jaiswal.
</script>

Output:

4

Time Complexity: O(N)
Auxiliary Space: O(1)